1. Evaluate ∫(0-4) x/√x^2+9 dx
2. Given F(x)= ∫(0-x) t√t^2+4 dt, find F'(x)
#1
Let
u = x^2+9
du = 2x dx
and you have
∫ 1/2 √u du
That's easy, right?
From the 2nd Fundamental Theorem of Calculus,
F'(x) = f(x) = x√(x^2+4)
2. Given F(x)= ∫(0-x) t√t^2+4 dt, find F'(x)
Let
u = x^2+9
du = 2x dx
and you have
∫ 1/2 √u du
That's easy, right?
From the 2nd Fundamental Theorem of Calculus,
F'(x) = f(x) = x√(x^2+4)